Point A is at #(2 ,-6 )# and point B is at #(-2 ,-7 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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Feb 22, 2018

Answer:

Increase in distance due to rotation of A is #d = 9.8085#

Explanation:

#A (2,-6), B (-2,-7)#. Rotated about origin by #(3pi)/2# clockwise.

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#vec(AB) = sqrt((2+2)^2 + (-6+7)^2) = 2.2361#

#A((2),(-6)) -> A’((6),(2))#

#vec(A’B) = sqrt ((6+2)^2 + (2+7)^2) = 12.0416#

Increase in distance due to rotation of A is

#d = 12.0416 - 2.2361 = 9.8085#

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